There have been many cases where the band or artists have done a live album in the studio, so there’s nothing new behind that one. I suspect half of the punk scene was recorded this way.
There are some other interesting cases, such as Todd Rundgren‘s album Nearly Human that was recorded as a single take in the studio, and his follow-up album 2nd Wind that was recorded in one take in front of a live audience — that was instructed to be dead-silent during the recording. This was indeed a tough challenge, one take and nail it down, as the music on those albums are very complex.
Another interesting angle was what Frank Zappa did with his live material, he mixed it together with studio recording material, so sometimes it was hard to know if what was what; a guitar solo was taken from a live situation where the rest was done in the studio, and so forth.
I’m actually looking at a future project where I want it all to sound very much live, but it’s all done in the studio. So I’m just now in research mode finding out how to produce and mix such an album. The obvious choice is of course to add in ambient audience sounds, but there’s more to it, such as emulating the guitar stacks mic:ed with reflections. So I suspect there will be a lot of Logic’s Space Designer as well as amp simulation that is needed to get this kind of sound. It will be interesting.